Journal of Geophysical Research: Oceans

Hindcasting the Adriatic Sea near-surface motions with a coupled wave-current model


  • M. Dutour Sikirić,

    Corresponding author
    1. Department of Marine and Environmental Research, Rudjer Bos˘ković Institute, Zagreb, Croatia
      Corresponding author: M. Dutour Sikirić, Department of Marine and Environmental Research, Rudjer Bos˘ković Institute, Bijenic˘ka 54, 10000 Zagreb, Croatia. (
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  • A. Roland,

    1. Institute of Hydraulic and Water Resources Engineering, Technische Universität Darmstadt, Darmstadt, Germany
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  • I. Tomaz˘ić,

    1. Department of Marine and Environmental Research, Rudjer Bos˘ković Institute, Zagreb, Croatia
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  • I. Janeković

    1. Department of Marine and Environmental Research, Rudjer Bos˘ković Institute, Zagreb, Croatia
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Corresponding author: M. Dutour Sikirić, Department of Marine and Environmental Research, Rudjer Bos˘ković Institute, Bijenic˘ka 54, 10000 Zagreb, Croatia. (


[1] Prediction of near-surface dynamics is one of the most challenging problems in oceanography because of the combined effects of waves, currents and turbulence. In this work an implementation of the Regional Ocean Modeling System (ROMS), two-way coupled to the Wind Wave Model II (WWM II), is used as the computational platform for the numerical experiments designed to evaluate the wave contribution to dynamics in the near surface region. To that end we apply recent concepts in physics of spectral wave modeling to close the momentum balance in the surface boundary layer. To force the ROMS and WWM II models and to assess their modeling skill we use observations and model results made during 2002–2003 in the Adriatic Sea. When all effects were included in the simulation, comparison with top-bin Acoustic Doppler Current Profilers (ADCP) measurements showed certain improvements. The mean error is reduced at most stations and the root mean square error decreased by 11% at all ADCP moorings and by 24% at four of them but the errors remain large due to the errors of the wind forcing. Our results also point to the importance of computing the Stokes drift from the full wave spectra instead of using a simplified truncation formula.

1. Introduction

[2] Prediction of motion in the near sea surface layer is of great practical importance but still remains a difficult problem to solve. It is of interest for oil spill predictions or search and rescue operations as well as for gaining further insight into the ocean surface dynamics. In the surface layer an often ignored contribution comes from the wave-current interaction. For example, in assessing the importance of the current-wave coupling,Jorda et al. [2007] found that at basin scale currents have no significant influence on the wave forecasts, whereas the wave impact on currents is much more pronounced, particularly through the modification of the wind drag coefficient. Traditionally, circulation and waves have been modeled separately. Dykes et al. [2009], for example, ran the SWAN (Simulating Waves Nearshore) wave model in real-time, using wind inputs generated by the ALADIN 8-km atmospheric model, to provide surface waves forecast for the Adriatic Sea in support of the Dynamics of the Adriatic in Real Time (DART) field experiments. The authors report success in simulating the spatial gradients in significant wave height (Hs) observed by in situ and remote-sensing measurements during a sirocco - southern wind event. It was also found that, compared to previous reports, use of higher-resolution wind forcing and more realistic orography reduced the underestimate of 10 m wind, but did not correspondingly change the magnitude ofHs. They concluded that a better wave model and wind-wave coupling would yield better results.

[3] In 2002–2003 a multidisciplinary oceanographic research program was undertaken in the Adriatic Sea [Lee et al., 2005]. Acoustic Doppler Current Profilers (ADCPs) were deployed in the northern Adriatic Sea. The Eastern Adriatic Current (EAC) and Western Adriatic Current (WAC) were analyzed in Book et al. [2007] and the WAC was found to be highly dependent on bursts of strong wind forcing.

[4] In a previous study using ADCPs at 57 m depth [Book et al., 2005], it was found that the WAC was highly barotropic during the winter of 2001. Following this, in Kuzmić et al. [2007]the northern Adriatic circulation in the winter 2003 was analyzed using two models. It was found that the barotropic and baroclinic models gave comparable results. The gyre were effectively reproduced, when the atmospheric forcing was from the 4 km Coupled Ocean/Atmosphere Mesoscale Prediction System (COAMPS). However, it was found that European Centre for Medium-Range Weather Forecasts (ECMWF) wind forcing failed to properly take into account the orographic effect of the Dinaric Alps and henceforth failed to reproduce the gyre.

[5] The ECMWF, COAMPS and Limited Area Model Italy (LAMI) wind forcings were evaluated in Signell et al. [2003] against the data collected at the Acqua Alta station (see station VR1 on Figure 1). It was found that the use of local area model decreases the underestimate of wind magnitude but that the local area model wind fields have a lower correlation than ECMWF wind fields. This was interpreted by the fact that large-scale features can be determined deterministically while small-scale features can only be determined stochastically. The winds in February 2003 were investigated using meteorological station and gas rig data inDorman et al. [2006] against the COAMPS hindcast. It was found that there is a strong variability over the northern Adriatic for each bora jet. The Senj jet was found to be the strongest, while the Trieste one can extend over the northern part of the Adriatic Sea.

Figure 1.

The Adriatic Sea with the bathymetry (isolines at 20, 35, 50, 100, 150, 200 and 800 m) ADCP positions (blue point) and gas rigs (red stars) used for comparison with model results.

[6] Paklar et al. [2008] used the Princeton Ocean Model [Blumberg and Mellor, 1987] and two mesoscale numerical weather prediction models to simulate trajectories of two satellite-tracked drifters during the summertime bora episode of 22–25 June 1995. The study revealed the need to increase the drag coefficient in order to reproduce adequately the effects of the sea surface roughness and the impact of the atmospheric conditions. This suggests a need for re-examination of the surface stress parametrization.

[7] Concerned with accurate numerical prediction of the ocean upper layer velocity, Carniel et al. [2009]assessed the effects of vertical resolution, different vertical mixing parametrizations and the sea surface roughness values on surface layer turbulent kinetic energy injection from breaking waves. The Generic Length Scale (GLS) turbulence closure formulation in the Regional Ocean Modeling System (ROMS) circulation model was modified accordingly. With the sea surface roughness allowed to depend on significant wave height the SWAN wave model was used. The model was used in the Adriatic Sea in which numerical drifters were released during an intense episode of bora wind (mid-February 2003). The model trajectories were compared to the paths of four satellite-tracked drifters deployed during the related field campaign. The inclusion of the wave breaking process helped to improve the accuracy of the numerical simulations, in addition to wave breaking parametrization and k-epsilon turbulence closure. An extremely high value of the Charnock sea constant (56,000) was used.

[8] The aim of this study is to further investigate the impact of wave-current interactions on the Adriatic Sea (seeFigure 1) surface currents by employing an up-to-date wave model and the wave-current coupling ofBennis et al. [2011], which is based on the explicit Lagrangian mean formulation [Ardhuin et al., 2008b]. The effort is akin to the work of Uchiyama et al. [2010]in which the wave-current interaction is explored employing a vortex-force formalism, ROMS circulation model [Shchepetkin and McWilliams, 2005] and the SWAN wave model.

[9] The rest of the paper is organized as follows. In Section 2 the models and data are briefly presented. The physical bases of the coupling procedure is described shortly in Section 3. Motivation and the setup of the performed numerical experiments are laid out in Section 4, while results of the experiments are discussed in Section 5 and summarized in Section 6.

2. Models and Data

[10] The ROMS model is a finite difference, free surface model that solves the primitive equations on curvilinear grids using the Boussinesq and hydrostatic approximations. It uses the time splitting method for time integration to resolve the numerical constraints related to the CFL criteria of gravity waves. The model uses a sigma-coordinate in vertical, which implies an intrinsic error in computation of the horizontal pressure gradient, for which several possible schemes are proposed [Shchepetkin and McWilliams, 2003]. In accordance with the philosophy of giving the choice to the user to create the best setup for specific application, several schemes are available for bottom stress, surface stress, turbulence parametrization, boundary condition, advection and diffusion. The detailed setup of the model to the Adriatic Sea is explained later.

[11] The Wind Wave Model II (WWM II) model [Roland, 2008] is a wave model based on the WWM I [Hsu et al., 2005] using new numerical schemes, revised physics and more efficient algorithms. A fractional time step method according to Yanenko [1971] is used for time integration. The numerical methods for the advection of wave action in geographical space are based on the residual distribution schemes [Abgrall, 2006] and formulated using implicit or explicit time integration up to 2nd order accuracy in space and time. The integration in spectral space is done as in the WaveWatch III model [Tolman, 1992] by application of the ultimate quickest approach given by Leonard [1991]. For nonlinear triad wave interactions the Lumped Triad Approximation [Eldeberky and Battjes, 1995] is used, whereas the quadruplet interactions are approximated based on the Discrete Interaction Approximation according to Hasselmann et al. [1985]. With respect to the source terms, WWM II includes a variety of wind input and white capping parametrizations. We used the Ardhuin et al. [2010]parametrization both for wind input and dissipation and the wind-wave growth parameterBβ to 1.31 according to Ardhuin et al. [2011].

[12] Both ROMS and WWM II models were forced using the outputs from the LAMI [Cacciamani et al., 2002], a 7 km horizontal resolution and 35 vertical levels implementation of the meteorological fully non-hydrostatic Lokal Model originally developed by the German meteorological service [Steppeler et al., 2003]. Initial and boundary conditions are obtained from the DWD global circulation model GME [Majewski et al., 2002]. LAMI saved outputs every 3 h and produces a 48 h forecast. In our case we use forecasts at 03, 06, …, 24 h for 2 m air temperature, 2 m humidity, surface air pressure, 10 m wind, longwave and shortwave radiation. The meteorological fields were available from 18th of September 2002 until the 1st of June 2003 and were linearly interpolated onto the ROMS ocean model grid to provide the needed forcing. In order to estimate the LAMI wind predictive skill we compared the model results with available satellite QuikSCAT scatterometer estimates, ENVISAT altimeter data along with in situ measurements. QuikSCAT data provides high resolution neutral sea surface wind fields at 10 m height [Von Ahn et al., 2006] at 12.5 km horizontal resolution by using a geophysical model function. The related data were obtained from the Physical Oceanography Distributed Active Archive Centre (PO.DAAC) as a Level 2B Product ( and were limited to the Adriatic Sea. The 10 m neutral winds were computed from the 10 m ones using the COARE [Fairall et al., 2003] parametrization which uses stability functions from Fairall et al. [1996] with profile constants from Grachev et al. [2000] and stable form as in Beljaars and Holtslag [1991]. One has to keep in mind that in reality we are comparing one model results with another model since QuikSCAT does not measure wind directly. For altimeter comparison we used the ENVISAT satellite estimates of significant wave heights and 10 m winds. The estimates are done in ascending and descending tracks at 5 km resolution every 3 days. Data were obtained from the GlobWave project and the validation is detailed in Queffeulou [2004].

[13] In situ measurements for wind and Hswere recorded at several Italian gas rigs. However, after visual screening and basic quality checks, we used only five stations (Ada, Barbara-C, Fratello-C, Giovanna, Pennina shown onFigure 1). A detailed description of the platforms is given on Table 1. Unfortunately, we know only the height of the anemometer and we do not have more precise information on the position and settings of the anemometer and measuring device. When the wind measurements were done at a different height from 10 m we used the procedure described in Bidlot et al. [2002] in order to get 10 m wind by assuming neutrality and a Charnock coefficient of 0.018. Four of these stations also had wave measurements and we used additional measurements of wind and Hs at the Acqua Alta meteorological station [Cavaleri, 1999] (see VR1 on Figure 1).

Table 1. Description of the Stations Used for Wind and Wave Comparisona
Ada45.18 N 12.59 E15 mWind, HsGas ridge
Barbara-C44.08 N 13.78 E30 mWind, HsGas ridge
Fratello-C42.61 N 14.17 E21 mWindGas ridge
Giovanna42.77 N 14.46 E50 mWind, HsGas ridge
Pennina43.02 N 14.16 E40 mWind, HsGas ridge
Acqua Alta45.31 N 12.51 E15 mWind, HsPlatform

[14] The current data originated from an array of RD Instruments (RDI) Workhorse Sentinel broadband ADCPs. They were deployed in the northern Adriatic Sea from September 2002 to May 2003, as part of a joint research effort of several international collaborating teams [Lee et al., 2005]. The moorings consisted of 16 trawl-resistant bottom-mounted ADCPs distributed along portions of four mooring sections, with one additional ADCP off the west Istrian coast and another one mounted near the base of the meteorological tower Acqua Alta (VR1). The mooring positions are shown onFigure 1, top-most layer depth and bin-sizes are given onTable 2. For ADCP instruments on the SS, CP and KB line sampling were in the so called “burst” mode (every 10 or 15 min the ADCP measures as fast as possible instantaneous velocity) in order to minimize high frequency currents. For IC ADCP we used equally distributed sampling rate within 15 min interval giving 15 min mean currents as opposite to the rest of ADCPs observing every 15 min instantaneous velocities. Further details are available from Book et al. [2007] and Kuzmić et al. [2007].

Table 2. ADCP Depth, Depth of the Top-Most Layer, and Bin Sizea
NameDepth (m)Depth of Top-Most Layer (m)Bin Size (m)
  • a

    The ADCP locations are shown on Figure 1.


3. Wave Modeling and Models Coupling

[15] The theory of radiation stress was initiated by Longuet-Higgins and Stewart [1964] where a barotropic formulation of the stress created by difference in wave energy was found for the shallow water equations. A baroclinic formulation for the primitive equations was proposed by Mellor [2003], afterward criticized by Ardhuin et al. [2008a], who proposed another formulation [Ardhuin et al., 2008b] using the Generalized Lagrangian Mean (GLM) [Andrews and McIntyre, 1978]. In this formulation the model computes the quasi-Eulerian velocities, and the Stokes drift is added to the advection of tracers and momentum.

[16] Sinusoidal surface water waves are usually described by their wavenumber k, intrinsic circular angular frequency σ and absolute frequency ω. For a given depth d and surface current u the linear dispersion relation is σ2 = gk tanh(kd) with the Doppler shift relation characterized as ω = σ + u · k. According to the stochastic approach of modeling surface waves, in a more complete sense, waves in a field are defined with wave action N(x, k) at a spatial position x and wave number k. Using spectral space coordinates σ, θ for the energy we get the Wave Action Equation (WAE):

display math

The second term in the WAE is the advection part in geographical space, the third and the fourth terms represent the spectral advection part due to variations in the depths and the flow field. The source term Stot in the equation can be decomposed into different contributions; wind part Sin, the nonlinear interaction in deep and shallow water (Snl4 and Snl3), the energy dissipation due to white capping, bottom induced wave breaking and bottom friction (Sds, Sbr and Sbf). Summarizing the left side terms into the total derivative we can write

display math

By integrating the WAE one can compute the spectral wave density and thus get statistical values such as significant wave height, zero-crossing wave period, etc. The free surface elevation originating from the circulation model is present in the dispersion relation for waves. FollowingCavaleri et al. [2007] the advection velocity uA is modeled by the surface current. Another approximate approach would be to average the baroclinic velocities with respect to the vertical profile given by the mean wave length [Kirby and Chen, 1989]. However, modeling of the vertical sheared current effect is still missing and would require an adaptation of the exact WAE of Andrews and McIntyre [1978]. The effect of currents on the advection of wave energy is expected to be small with respect to the group velocity.

[17] In our approach of modeling effect of waves on the currents we used the Bennis et al. [2011] formulation, which is a simplified version of Ardhuin et al. [2008b]. Using that approach one can decompose the total velocity field utot as a sum u + uwave + uturb. This is possible under the assumption that circulation u and wave current uwave are statistically independent of the turbulent velocities uturb. The mean Eulerian velocity field of the wave velocity uwave is zero, but the related resulting movement of a Lagrangian particle is not, hence Stokes drift us. If one assumes that the turbulent velocities are negligible with respect to the global circulation and are independent of the wave motions, i.e. neglect Langmuir circulation [McWilliams et al., 1997], then the formalism describing combined circulation and wave movement is accomplished through the GLM.

[18] In our nomenclature we used h for depth, ξ for the free surface elevation and d = ξ + h for the dynamic depth. The horizontal Stokes drift can be expressed as an integral over the wave spectrum E (k) = σN(k) as

display math

If only significant wave height Hs, mean wave length L and mean direction θ are available, then the Stokes drift can be computed by a simpler truncation formula as

display math

with σL the mean angular frequency computed from Land the dispersion relation. On the other hand, in an environment of varying depth, spectrum or current, in order to guarantee the non-divergence of the Stokes drift, it is necessary to introduce the vertical Stokes drift in the following way:

display math

The Stokes drift current us = (us, vs, ws) must be added to drifter trajectories when integrating in time to get their position. Also, the GLM vertical position of a surface drifter is

display math

It is the vertical position of a surface drifter when one applies local temporal means in order to remove the wave variability. If we write u = (u, v, w), then we can define the material derivative

display math

Using the defined Stokes drift, we can write down the conservation equation for tracers like temperature, salinity or turbulent kinetic energy

display math

with C(T) as source or sink of tracers T and D(T) the diffusion. In that case wall boundary conditions u = 0 should be replaced with u = −usand similarly for other types of boundary conditions. The Stokes drift also enters into the computation of the advection of the Quasi-Eulerian momentum:

display math

Fpres and Fturb are the pressure and turbulence terms respectively, while Fcor = fcor (v + vs, −uus) is the Coriolis term with fcor the Coriolis factor. We follow Bennis et al. [2011]in replacing the wave-induced mean pressure termJby a two-dimensional approximation:

display math

The wave forcing term Fwave is expressed as:

display math

The equation for the surface elevation ξ is rewritten using the Stokes drift as

display math

A wave formulation of the bottom stress Fbottom is proposed by Bennis et al. [2011]. That is, if the wave bottom boundary layer were resolved, then the appropriate boundary would be (u, v)|z=−h = 0 and Fbottom would be obtained from the integral of the term Sbf in equation (2); see Bennis et al. [2011] for more details. In this work we use instead a quadratic form for the bottom stress described later.

[19] Wave information can also be used for modeling the sea roughness length. One classical approach [Terray et al., 1996; Burchard, 2001; Janssen, 2010] is z0,sea = cHs but the value of c is still open to discussion. It is generally assumed [Janssen, 2010] that c = 0.5 but field experiments [Burchard, 2001] indicate that c = 1.5 is more plausible. Another classic parametrization uses the Charnock coefficient αsea, i.e. z0,sea = αseaτ / (ρsea). Usually the parameter αsea has value of 1,400 but higher values (i.e. 56,000) are possible and were considered by Carniel et al. [2009].

[20] The surface stress Fsurf is usually modeled according to the meteorological parameters 10 m wind speed, 2 m air temperature, and 2 m relative humidity [Fairall et al., 2003]. Janssen [1989] decomposed the surface stress into viscous stress, wave stress and high frequency stress. Viscous stress is generally small, wave stress is computed from the wave spectrum, while Janssen [1989] provides a parametrization of the high frequency stress. In our approach we use the surface stress from the wave model in order to force the circulation model. This way is actually inconsistent in the sense that, if we change the stress, then we should also change the stress used in the meteorological model, but for this we would need to have three coupled models which is beyond the scope of the present study. Furthermore surface currents also have an impact on the surface drag and the wind profile [Hersbach and Bidlot, 2008]. Paskyabi et al. [2012] proposed a slightly different formulation for the momentum input by having an exponential profile for the momentum from wave dissipation instead of concentrating the stress on the surface as in Bennis et al. [2011]. Saetra et al. [2007] reported improved forecasts when using a surface stress obtained by integration of the wave surface stress instead of using only the wind and air density. As a consequence we have used the Ardhuin et al. [2010] formulation of wave stress, which after integration gives the stress applied to the model.

4. Setup Used in Numerical Experiments

[21] The Adriatic Sea (see Figure 1) is a narrow epicontinental basin characterized by only one open boundary at the Otranto strait through which it is connected with the Mediterranean Sea. The northern part of the Adriatic Sea is a shallow (<50 m) region while the middle and southern Adriatic have depths up to 250 m and 1200 m, respectively. Its eastern side is characterized by a complex coastline with many islands and narrow, sometimes very deep, straits. Complex orography surrounding the Adriatic Sea (Dinaric Alps on the East, and Apennines on the West) contributes to two dominant Adriatic winds: the cold and dry cross-basin bora, blowing from East - North-East direction over Dinaric passes, and the warm along-basin, long-fetch southerly sirocco. Both winds can generate large waves.

[22] The curvilinear Adriatic grid, used by the ROMS model, is characterized by ≈4 km horizontal resolution. It is the same one as used in Carniel et al. [2009] but with small modifications in order to better resolve bathymetry and coastline. Furthermore, the bathymetry was smoothed according to the method proposed by Dutour Sikirić et al. [2009]. The vertical discretization within the ROMS model is composed of 20 vertical layers and uses a nonlinear stretching function, which generalizes the one of Song and Haidvogel [1994]. This stretching function depends on some parameters, a thermocline parameter hc and the bathymetry h. The parameters are set in order to fit as closely as possible to the surface and it is a common practice to set hc to the expected depth of the thermocline, i.e. 20 m in the Adriatic Sea. This results in a top layer thickness of 10 cm in the shallowest part of the Adriatic Sea, at most 67 cm in the northern part and 1.26 m in its deepest part. For the WWM II model we used an unstructured finite element mesh obtained directly from the finite difference ROMS grid by subdividing the cells. The wave and circulation models were integrated with a 150 sec time step which was also chosen as the coupling time interval in order to maximize coupling effects between models. The open boundary conditions at the Otranto strait are modeled using the Chapman [1985] and Flather [1976] formulation for free surface and barotropic velocities. For baroclinic velocity and tracers, we used daily averaged fields from the Mediterranean Forecasting System (MFS) [Pinardi et al., 2003]. An estimate of 7 harmonic tidal constituents is available from Janeković and Kuzmić [2005] and the tidal signal is added to current and free surface at the open boundary. The advection of tracers is done by the multidimensional positive definite advection transport algorithm Smolarkiewicz and Margolin [1988], while the 3rd order upwind scheme is used for momentum. See Janeković et al. [2010] for more details.

[23] Since we are not sufficiently resolving the bottom boundary layer, we cannot use the wave boundary condition for the bottom, which is why we use a quadratic form for the bottom stress with a constant obtained from the logarithmic profile. For the turbulence parametrization, we use the gen parametrization [Umlauf and Burchard, 2003]. The Craig and Banner [1994] formulation is used for the parametrization of the surface turbulent kinetic energy. In order to parametrize the surface stress we can either use the COARE parametrization, or following Bennis et al. [2011], the spectrally integrated surface stress of the Ardhuin et al. [2010] formulation. However, we still used the COARE bulk flux formulation [Fairall et al., 2003] for air-sea exchange of heat. This means that the ROMS model is using a separate turbulent formulation for the air-sea exchange of momentum and in particular that information from the wave model is not used for improving the heat exchange. One possible approach could be to use theJanssen [2010] formulation and/or to couple the ROMS with a meteorological model [Warner et al., 2010], but this is beyond the scope of this work. The main problem, apart from the forcing, is probably the insufficient resolution, which is especially problematic for the islands on the eastern coast.

[24] In our formulation the wave model influences the circulation model in three ways: (I) The significant wave height is used in the computation of the sea roughness length. (II) The Stokes drift dynamics is also used in the advection of tracers, momentum and as a radiation stress term inside the primitive equations. Finally (III) the surface stress is obtained from the wave model.

[25] In order to quantify the relative importance of the contributions that have been implemented, we have done several experiments:

[26] Experiment 1 is the basic ROMS model integration where we do not use any wave dynamics. For this experiment we have used the Charnock relation for computing the sea roughness length z0,sea with αsea = 1,400 which is the commonly used value.

[27] Experiment 2 is the same as (1) with additional formulation for sea surface roughness length as z0,sea = 0.5 Hs.

[28] Experiment 3 shares the same setup as (2)with the Ardhuin formulation used for the coupling wave-ocean according to formulas(8), (9), (11) and (12).

[29] Experiment 4 is the same as (3) except that we used the surface stress computed from the wave model rather than from COARE bulk flux formulation of Fairall et al. [2003].

[30] Table 3 gives a short description of the four experiments. Using that incremental approach, each experiment allows us to estimate the relative contribution of the newly introduced terms. In Experiment 4 we are estimating the cumulative effects of all contributions. However, since the contributions, except the first one, are relatively small, we can actually discuss their individual effects separately, without having to consider all eight possibilities.

Table 3. Brief Description of the Four Experiments (Exp.) Used in This Work
 Exp. 1Exp. 2Exp. 3Exp. 4
Sea roughness lengthz0,sea = αseaτ / (ρsea)z0,sea = 0.5 Hsz0,sea = 0.5 Hsz0,sea = 0.5 Hs
Radiation stressnonenoneformulas (8), (9) and (11)formulas (8), (9) and (11)
Surface stressbulkbulkbulkwave

5. Results and Discussion

[31] As mentioned before the validation data comes from the period January-February 2003. During this period the most energetic wind was the bora with several pronounced long lasting episodes. At the opposite, sirocco events were rare, lasting usually only one day. In all our numerical experiments the circulation was the typical one for the winter period [Cushman-Roisin et al., 2001] characterized by the southward/outward colder WAC flowing along the Italian coast, and the warmer northward/inward EAC flowing along the Croatian coast. During the strong and lasting bora episodes, the well known formation of a multiple gyres current regime in the northern Adriatic Sea was well established [Kuzmić et al., 2007]. The WAC was enhanced during the bora episodes [Ursella et al., 2006] while the EAC was increased during the sirocco cases.

5.1. Idealized Test Case of Shoaling

[32] In order to test our implementation, we used the adiabatic test case of Bennis et al. [2011]: waves of significant wave height 1.02 m and period 5.26 s shoaling from 6 to 4 m and then again from 4 to 6 m depth (Figure 2). The waves induce both Stokes drift and quasi Eulerian currents. The coupled model is run without nonlinear interaction, dissipation or wind input on a numerical 1-dimensional periodic grid. Temperature and salinity are assumed constant and only a background vertical mixing of 1 · 10−6 m2/s is used for momentum. The horizontal resolution is 8 m and 40 equally spaced vertical levels were used during simulations. Results for significant wave height, baroclinic currents and barotropic currents are shown on Figure 2.

Figure 2.

Shoaling test case between 4 and 6 m with incident monochromatic waves of significant wave height 1.02 m and period 5.26 s. (a) Significant wave height, (b) total Lagrangian current, and (c) barotropic Stokes and quasi Eulerian currents.

[33] This case illustrate nicely, actually without any computation, the need for the vertical Stokes drift. First of all it is apparent that, in case of shoaling, the Lagrangian trajectories have to go upward and that a vertical Stokes correction must be present. Secondly, if one integrates vertically the horizontal Stokes drift, either from equation (3) or (4), then one gets that the total vertical flux is not conserved when the depth changes, even assuming no dissipation. But the non-divergence of the Stokes drift, means that the difference in flux between two vertical profiles of different depths has to be compensated. This cannot happen on the bottom where the flux is zero so it must be on the surface. Let us assume, for the sake of argument, steady state and horizontal free surface. Then usingequation (12) one gets that w + ws = 0 at the surface. This means that the vertical Stokes drift at the surface is exactly compensated by the quasi Eulerian component and that the Lagrangian flux D(ū + ūs) is constant. In the case of the experiment, it is found to be equal to 0.124 m2/s. Having said that, the absence of any dissipation makes this case highly artificial with induced currents propagating infinitely from the shoaling.

5.2. Comparison With Scatterometer, Altimeter and In Situ Data

[34] The quality of the input wind is a fundamental part of any simulation of wind/wave/ocean dynamics [Bertotti and Cavaleri, 2009]. In order to estimate the LAMI wind quality we used satellite QuikSCAT scatterometer, ENVISAT altimeter and in situ measurements. Using the QuikSCAT data in assessing the model wind quality allowed us to estimate also atmospheric model spatial errors, something that could not be done using only spatially sparse in situ data. QuikSCAT instrument specifications give zero bias both for the magnitude and direction and Root Mean Square Errors (RMSE) of 2 m/s for magnitude and 20° for direction. However, validation studies with in situ data in coastal regions [Tang et al., 2004] (<80 km) show that while the wind speed is still within specification (0.93 m/s ± 1.83 m/s) the wind direction is not (4.71° ± 31.15°). For light winds (<3 m/s) these errors are even higher, especially for wind direction. In order to compute these errors model wind data was interpolated in time onto the specific time of QuikSCAT pass over the Adriatic Sea and then subsampled onto the QuikSCAT grid. Overall spatial distribution of error was derived by averaging differences between model and interpolated QuikSCAT neutral wind magnitude and direction for each QuikSCAT pass. Based on data, maps were derived for mean and standard deviation fields by using the whole time period (Figure 3).

Figure 3.

Spatial fields of the difference between LAMI model and QuikSCAT data for January-February 2003. (a) Wind magnitude bias (m/s), (b) wind magnitude standard deviation (m/s), (c) wind direction bias (deg) and (d) wind direction standard deviation (deg).

[35] Finally, statistical estimates for bias were derived as difference between LAMI model and QuikSCAT or in situ values, showing that in the period considered LAMI underestimates wind magnitude (−0.24 m/s) when compared against QuikSCAT measurements (total number of samples used in the analysis was 3 · 105) and overestimates it (0.63 m/s) when compared to the in situ measurements (total number of used records was 13 · 103). Standard deviations are similar for both QuikSCAT and in situ data (≈3.0 m/s). Overall direction bias is positive for both QuikSCAT and in situ data (13° and 5°), while standard deviations are smaller for QuikSCAT (45° versus 70° for in situ). Comparison between ascending/descending pass of the QuikSCAT satellite shows no significant difference in the results.

[36] General spatial wind magnitude differences (Figure 3a) are highly correlated with areas of higher or lower wind speeds of the bora jets and are in a range between −3 and 3 m/s. The highest positive errors are correlated with lower overall mean wind magnitude, except in the southern Adriatic Sea, where this error is correlated with the higher mean wind magnitude. Underestimate of the model wind magnitude fields (negative bias) is correlated with a higher mean wind magnitudes (i.e. Kvarner and S˘ibenik regions strongly under the influence of bora). Wind magnitude standard deviation ranges from 3 to 5 m/s with the highest values in the middle and central parts of the Adriatic Sea. The bias for wind direction is found to be the largest near the eastern coast. A possible explanation for that is that the effect of insufficient resolution of the atmospheric model is especially sensible on bora jets. The standard deviation is relatively uniformly distributed around the whole domain (≈35°), with a higher values around the Italian coast (≈55°) and around the south-east Adriatic coast (≈70°). Scatter density plots of the LAMI model wind magnitude and direction compared to QuikSCAT (Figures 4a and 4b) and in situ ones (Figures 4c and 4d) shows relatively low correlation (0.7) for wind speed. It also points that while the LAMI model generally underestimates wind speeds, it tends to overestimate them in the range 15–20 m/s. The bias in wind direction is apparent for QuikSCAT but more complex for in situ stations. There is a systematic bias at the Acqua Alta stations and a fixed direction at Fratello-C giving the straight line in the scatter plot, which is likely to be an artifact. When restricting to wind speeds of more than 10 m/s we found that the bias in direction for QuikSCAT decreases to 8° and the standard deviation to 30°. We found also that no such error reduction happens for in situ stations, which indicates that errors are more likely to be related to measurements.

Figure 4.

Scatter density plots between LAMI model and (a) QuikSCAT wind magnitude (m/s) data, (b) QuikSCAT wind direction (deg), (c) in situ wind magnitude (m/s) and (d) in situ wind direction (deg).

[37] The radar altimeter of the ENVISAT satellite provided significant wave height and surface 10 m wind estimates. The quality of estimated significant wave height of ENVISAT was assessed in Durrant et al. [2009] using buoy data. It was found that, over the ocean, low Hs are overestimated and high Hs underestimated and that the root mean square difference is about 22 cm. The quality of ENVISAT wind field was assessed in Abdalla [2006] against model and buoys data. It was found that the global bias in wind speed is about 15 cm/s when compared to the model and about 65 cm/s compared to the buoy data. The wind speed scatter index is about 17% when compared to the model and about 18% compared to the buoy data. One has to keep in mind that it was a global analysis that does not necessarily apply to the Adriatic Sea. Note also that the wind fields are estimated from the surface stress and thus do not take into account the surface currents [Hersbach and Bidlot, 2008].

[38] Results of comparison for scatter plot of altimeter estimated wind speed and Hs with respect to the LAMI model and Hs computed in experiment 4 is shown on Figure 5. The mean bias for Hs was found to be 11 cm and the RMSE 54 cm. The mean bias for 10 m wind was found to be 1.01 m/s and the RMSE 3.26 m/s. In a number of events we found that the modeled peak wind speeds are higher than the measured ones which impacts directly the Hs. This tends to confirm the result of QuikSCAT analysis, however the mean bias are of opposite sign. The difference is statistically significant but is within the above mentioned error estimates. The correlation and scatter index are found to be better for Hs than for the wind, which is as expected.

Figure 5.

(a) Scatter plot of 10 m ENVISAT wind estimate and LAMI winds; (b) the same for ENVISAT significant wave height estimate and ROMS-WWM II model results (m is the slope of the best fit, c the correlation and s is the scatter index).

[39] For the January–February period, scatter index of Hsat Acqua Alta is 0.31 but is 0.43 at the Ada, Barbara-C, Pennina and Giovanna gas rigs. The correlation is 0.85 at Acqua Alta and 0.90 at the other stations. TheHs is overestimated more at the gas rigs with a slope of best fit of 1.16 as opposed to 1.08 for Acqua Alta, which is possibly explained by the larger Hsat gas rigs. We found a systematic underestimate of zero crossing period at Acqua Alta, which may be explained by different cut-off frequencies between the station and the model. However, the mean wave direction is very well predicted with a negligible mean bias and a standard deviation of 20° despite having some error in the model wind direction at Acqua Alta.

[40] Signell et al. [2003] considered the LAMI, COAMPS and ECMWF wind speed forecast for the period March 1 to April 30 2001 and compared them with the Acqua Alta station. They found out that the underestimate of wind speed by local area models LAMI and COAMPS is 3 to 4 times less than the underestimate of wind speed by the ECMWF model. However, the correlation was found to be highest (0.72) for the ECMWF model. This was interpreted by the fact that a global model has less noise than a local model that behaves in a more stochastic way. In Cavaleri and Bertotti [1996] and Pettenuzzo et al. [2010] a procedure was proposed for correcting ECMWF wind fields by multiplying the speed by a constant or spatially varying scale factor. Cavaleri and Bertotti [1996] reported improvements for the modeled significant wave height when using the WAve Model (WAM) [Hasselmann et al., 1988] and the corrected wind fields in the Adriatic Sea. All this points to the need for better wind and meteorological forecasts over the Adriatic Sea. The LAMI model horizontal resolution at 7 km is clearly insufficient and needs to be improved. It is also clear from QuikSCAT ascending/descending results that the initial state and boundary forcing have to be improved. Lastly, following Cavaleri et al. [2012] one may need to couple the atmospheric model to a wave model in order to correct the surface boundary layer and obtain better results for wind and Hs.

[41] We used two periods of strong wind for the evaluation of the effect of waves on the modeling of surface currents. The first episode was from 7th to 13th of January 2003, characterized by a strong bora wind blowing across the Kvarner Basin providing a good basis for our comparison. The second bora episode was from 9th to 15th of February, slightly weaker, also occurring over Senj and Dubrovnik regions. The average significant wave height reaches 3 m in the Kvarner Basin for the first period and 2 m for the second period. The comparison with QuikSCAT indicates that the hindcast bora jets are inadequate around the Istrian peninsula region with 2.5 m/s errors positive or negative and with large deviations. However, the second bora period exhibits weaker winds and waves but a larger overestimate of winds near the Italian coast. The standard deviation of wind speed and direction is found to be 3.7 m/s for the first period and 2.9 m/s for the second period. The ENVISAT also shows mean bias of 2 m/s for the first period and −0.7 m/s for the second one but with the same mean bias in Hs of 7 cm for both periods and the RMSE less than 50 cm. For the first period, waves are generally overestimated at all stations by about 40 cm, while for the second period results are better with RMSE of 24 cm at Acqua Alta and higher at other stations. The underestimate of the zero crossing period at Acqua Alta is actually larger for the second period in despite the better forecast for Hs.

5.3. ADCP Comparison

[42] The ADCP moorings were predominantly located in the northern part of the Adriatic Sea, providing valuable observations of the currents throughout most of the water column. An ADCP by design measures currents using the Doppler effect, sampling the sea at a sphere lobe and should not be considered a single point measurement like e.g. the classical Aanderaa current meters. An ADCP provides velocity averaged over the sampled volume from, in our case, 4 beams. We limit our model to ADCP comparison only to the top-most measurement of surface velocity since we are interested foremost in surface wave/wind induced dynamics, which are the most pronounced in the surface bin data. The tidal variability was removed from model output and ADCP by using tidal constituent which were used as a forcing at the open boundary (K1, M2, S2, N2, K2, O1 and P1). ADCPs were measuring every 15 minutes the instantaneous currentsutot, except for the station IC, (see Table 2) in so called burst mode. IC used means over a 15 minutes period which means that, it could capture wave motion if the wave period matches with the sampling interval. Unfortunately, the mean wave periods are never very far from 5 s, which means that we cannot exclude that wave motions are captured by ADCP IC. However, a simple computation shows that the periods would have to be within 0.03 s for the effect to be significant hence we can compare the ADCP with the model quasi Eulerian velocities. In the case, the Stokes drift does not enter directly into this comparison. The ADCP locations are marked on Figure 1 while ADCP settings in Table 2. For this comparison we interpolated the model values at the geo-location of the ADCPs as well as at the same center depth of the top-most ADCP bin cell layer.

[43] Results for Root Mean Square Error (RMSE), Mean Absolute Error (AE) and bias (ME) are indicated on Table 4for the first bora period and for the magnitude of the top-most current. Results are significantly better for experiment 4 for stations KB1, CP3, CP5 and IC, which are directly exposed to the bora jet, but the errors remain relatively high for station IC, VR6, which are near the Istrian coast. For station VR1 and VR2, use of the sea roughness length leads to significantly better mean surface currents with a very small mean error and 30% smaller RMSE. For the ADCPs on the SS line we found worse results for SS2 and SS4 which are directly exposed to the WAC and have large currents. This indicates that the WAC is not adequately represented in the model which can be explained by highly varying bathymetry and density inside this region, hence introducing both physical and numerical problems. We suspect that the horizontal resolution of the model is likely to be the main cause of the problem. For other ADCPs on this line the results are mostly independent of the experiment. Overall we got 11% reduction in RMSE at all stations and a reduction by a factor of 4 for the sum of the mean error in the surface currents even though we have an increase of the mean error at stations VR5, SS2, SS4 and SS5. Magnitude of surface currents for the first period from 7th to 13th of January 2003 and four ADCP locations are shown atFigure 6. The results show improvement at the VR1 station, while VR5 is essentially unchanged. For the stations CP3 and KB1 there is a large reduction in the error, however the error still remain pretty big. For KB1 this is possibly due to the orographic and bathymetric effects which are difficult to resolve both by the meteorological and circulation models indicated in the wind comparison.

Table 4. Results for Comparison Between Surface Currents (cm/s) at the Top-Most ADCP Layer Against Four Numerical Experiments (Exp.) for the Period of 7 Until 13 January 2003a
 Exp. 1Exp. 2Exp. 3Exp. 4Mean CurrentNumber of Samples
  • a

    The experiments are described in Section 4 and Table 3. The ADCP locations are shown on Figure 1, and their setting is given in Table 2. Statistical values for the Root Mean Square Error (RMSE), Absolute Error (AE) and Mean Error (ME) are given.

VR4 RMSE10.59.910.110.112.1128
SS2 RMSE26.027.928.129.150.0142
SS4 RMSE14.615.615.415.742.3144
SS8 RMSE15.514.615.715.614.6145
SS9 RMSE10.19.910.510.415.9143
CP3 RMSE13.910.
CP5 RMSE22.717.617.317.021.9145
KB1 RMSE29.323.122.322.320.2140
total RMSE15.213.613.513.6  
Figure 6.

Detided current magnitudes from ADCPs in the top-most layer and experiments 1, 2, 3 and 4 for four stations and the period of 7 until 13 January 2003. The experiments are described inSection 4 and Table 3. The ADCP locations and settings are given in Table 2 and Figure 1.

[44] Results for mean surface current for this period and four experiments are shown on Figure 7. It is evident that, in general, when using the formulation z0,sea 0.5 Hsfor the sea roughness length (experiment 2) there is a small net decrease of the magnitude of the surface current. This is especially true for the southern tip of Istria region, but it also affects the northern Adriatic Sea near Venice and the Italian coast. When using Ardhuin formulation (experiment 3) we found no significant effects or improvements. Using the surface stress from the wave model (experiment 4) led to little increases in the surface currents near the Po mouth and the Italian coast but in general has not significantly changed previous picture. Similarly for the mean free surface and the same period (not shown), effects are small, in the order of 1 cm as one could expect. When computing the sea roughness length from the wave model (experiment 2) we saw a decrease in the current velocity, which induced a decrease of the free surface along the Italian coast. However, there is a corresponding increase of the free surface in the path of the bora jet. Similarly, using the Ardhuin formulation of wave-current coupling, we found only a slight increase near the Venice lagoon of free surface elevation due to wave setup. In our last experiment when using the surface stress from the wave model, we observed a decrease of the free surface near the Italian coast and a corresponding increase near Trieste and Dubrovnik region. This corresponds to a tendency of the wave supported stress to be slightly lower than results from the COARE formulation.

Figure 7.

(a) mean surface current magnitude for the period of 7th until 13th of January, 2003 and for experiment 1. (b) Effect of sea roughness length parametrization, (c) Ardhuin's formulation of radiation stress and (d) wave supported surface stress on mean surface current magnitude, i.e. mean surface current magnitude of experiments 1, 2, and 3 is substracted from mean surface current magnitude of experiments 2, 3 and 4. The Experiments are described in Section 4 and Table 3.

[45] When analyzing results for the second bora situation, shown in Table 5, we found significant differences. This time at the VR1 and VR2 stations we found larger errors when using wave formulations, both for ME and RMSE. Current magnitude was slightly decreased in the northern Adriatic Sea and results were mostly neutral there. Along the SS line the WAC was reduced which led to better results for the wave formulation. As before the impact on the rest of the SS line was not so pronounced. In the case of IC, KB1, CP3, and CP5 ADCPs the average current was 30% smaller and the improvement in a sense of the RMSE and ME comparatively smaller. Mean surface currents, shown on Figure 8, exhibit a smaller values near the tip of Istria, but a stronger bora induced currents in the southern Adriatic gyre (experiment 1). This southern current is modified in experiment 2 and the surface currents near the Istria were reduced as well. When using the Ardhuin formulation, we found a reduction of the surface currents near the Italian coast which was responsible for giving better results at SS2 station, and an amplification of the currents in the Southern Adriatic gyre. The formulation includes many different terms, but we believe that the one that is responsible for this behavior is the inclusion of the Stokes drift in the Coriolis force term. The use of surface stress from the wave model induces an increase of the currents in the southern Adriatic pit, where we found relatively large waves during the whole period. Due to the complexity of the process involved, we could not see any clear pattern when analyzing the free surface elevation. For the whole period we found a 9% improvement in total RMSE, which is possibly explained by smaller waves having smaller effects.

Table 5. Results for Comparison Between Surface Currents (cm/s) at the Top-Most ADCP Layer Against Four Numerical Experiments (Exp.) for the Period of 9 Until 15 February 2003a
 Exp. 1Exp. 2Exp. 3Exp. 4Mean CurrentNumber of Samples
  • a

    The experiments are described in Section 4 and Table 3. The ADCP locations are shown on Figure 1 and their setting is given in Table 2. Statistical values for the Root Mean Square Error (RMSE), Absolute Error (AE) and Mean Error (ME) are given.

SS2 RMSE12.711.48.88.922.489
SS4 RMSE11.310.513.314.719.0143
SS5 RMSE9.89.28.910.019.1142
CP3 RMSE14.611.111.210.710.3122
CP5 RMSE18.213.913.613.312.8145
KB1 RMSE26.522.321.621.312.1142
total RMSE11.910.210.310.4  
Figure 8.

Same as Figure 7, but for the period from 9th until 15th of February 2003.

[46] In general, the results show that setting the sea roughness length (our Experiment 2) has significant effects on the final results. If one uses the Charnock relation z0,sea = αseaτ/(ρsea), then one can get a sea roughness length of 30 m during the bora episode, which is unrealistic and leads to artificially large mixing [Takaya et al., 2010]. Our results are similar to Carniel et al. [2009] who found a large impact on surface velocity from the modification of the surface turbulent scheme.

[47] At the same time the Ardhuin formulation of radiation stress (our Experiment 3) led to only small changes for almost all ADCP measurements. The only ADCPs for which the effect is significant are SS2 and SS4 where it reached 10 cm/s. In the case of all other ADCPs those differences were very small.

[48] The use of the surface stress from the wave model, as in our experiment 4, did not produce significant effects on the overall results as one could expect. This may be explained by the fact that the COARE formulation, which was fitted for tropical seas [Fairall et al., 1996], is relatively adequate for the Adriatic Sea as well. In Saetra et al. [2007] waves were modeled according to a single point wave model, i.e. neglecting spatial advection, and the resulting surface stress was compared with a drag coefficient depending piecewise linearly on wind speed. The results showed strong improvement in storm surge situations for mean sea level, whereas in our case we find only small improvements. The point is that the COARE formulation uses thermodynamic information which is not used by the wave model and that, consequently, has a boundary layer physic that models gustiness and the stability term in the logarithmic wind profile. This makes our comparison not completely consistent and raises the question of whether one could derives a wind input formulation for wave models that uses thermodynamic information. One approach considered in Bidlot [2012] is to use only neutral wind in the wave model and to model the gustiness with the stability parameters. Another point is that their implementation of the wave stress is different from ours: the dissipated wave energy is inserted all over the vertical profile instead of only in the surface as for our parametrization. In Figure 9 the scatter plot of Charnock coefficient αair = gz0,air / v*2 is shown. It appears that the spreading by the wave stress formulation is much larger than the one from the COARE formulation providing more physical solution. It turns out that the wave formulation of surface stress that uses Ardhuin et al. [2010] gives a larger air roughness length than the COARE formulation. Together with the stability function term this explain the higher Charnock coefficients on Figure 9. In general, we found that the use of the surface stress from the wave model leads to a small reduction in the surface stress and consequently of currents.

Figure 9.

Charnock coefficient variability with respect to the wind input. Red for COARE [Fairall et al., 2003] bulk flux formulation and blue for wave supported stress [Ardhuin et al., 2010].

[49] An important aspect of our modeling is the use of Stokes drift obtained by integration over the spectrum by formula (3) as opposed to the truncation formula (4). Figure 10 shows results for surface Stokes drifts and the mentioned approaches along with a typical wave spectrum. It is apparent that the truncation formula led to higher Stokes drift magnitudes that are not fully realistic. A possible explanation is that the truncation formula does not account for the directional spreading of the wave spectrum. We think that this approach should be used only when no other possibility is available, but one should be aware that it can overestimate by a factor of 2 the Stokes drift in a regions where wind/wave dynamics is important.

Figure 10.

Model computed Stokes drift using (a) truncation formula (4) and (b) integration of wave spectra from formula (3) at 1st of January 2003 16:00 UTC.

6. Conclusions

[50] In this work we have explored the impact of combined circulation and waves modeling on predicting the near-surface motions in the (primarily northern) Adriatic Sea. To that end recent concepts in physics of spectral wave models have been used to close the momentum balance in the surface boundary layer. To force the ROMS and WWM II models and to assess their modeling skill, we have used the surface fields from the meteorological LAMI model for the period January-February 2003. In situ, scatterometer and altimeter wind data was used to assess the wind forcing, and ADCP data to estimate the skill of the ROMS-WWM II coupled system.

[51] Wind comparison shows that the wind forcing overestimates peak speeds and that errors are generally relatively large. The wind direction is found to have a significant bias near the eastern coast. The implementation of the two-way coupled ROMS and WWM II models was used as a computational platform for four numerical experiments. In the first experiment, designed to provide the baseline, no coupling to the wave model was implemented and the surface stress was modeled assuming the commonly used value ofαsea = 1,400. In the second experiment the wave model was coupled to ROMS and used to compute the sea roughness length as z0,sea = 0.5 Hs. This change alone had significant effects on the simulation and reduced the surface currents bringing model results closer to the observations. In the third experiment the wave stress was also included in the equations of motion. This yielded a significant change in the WAC and the South Adriatic gyre.

[52] In the fourth experiment, instead of the usually used COARE dependence, the surface stress was provided directly from the wave-model, which also led to small, but positive, changes in the final results. Since the COARE formulation uses thermodynamic information that are not used by the wave model, the comparison is not fully objective and simply indicates that it would be interesting to have a wave wind input formulation that fully uses thermodynamic information. Further investigation must be done using the WAM model physics used at the ECMWF, since it is known that the Charnock coefficient shows a larger scatter than the one presented here based on the Ardhuin formulation. The total RMSE decreased by 11% with reduction of 24% at four ADCP moorings. However, the errors remain large and we attribute them first of all to the inaccurate wind forcing for which the solution might be to have better global model, resolution and surface boundary layer physic. For the ROMS + WWM model, the main issues are insufficient resolution and need to improve the parametrization of turbulence. One of our results points to the need to compute the Stokes drift from the wave spectra instead of using the truncation formula whenever it is possible.


[53] This work has been supported by the Croatian Ministry of Science, Education and Sport under contract 098-0982705-2707. Authors are grateful to Luigi Cavaleri for providing wave data at Acqua Alta station, Rich Signell for preparing netCDF files with the meteorological data from Italian gas rigs, initial ROMS ADRIA02 grid and Jacopo Chiggiato for providing the LAMI atmospheric model data. We are thankful to Peter Janssen and Fabrice Ardhuin for useful discussions of the wave physics.